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 Proof of Anything (Posted on 2003-12-13)
Here is a nice little paradox:

Statement S: If S is true then God exists
Logically, statement S must be either true or false.

1. Suppose S is false.

2. If S if false, then any statement that starts with "If S is true..." is true *(see note)

3. Specifically, the statement "If S is true then God exists" would be true

4. This is exactly what S says, so S would have to be true

5. This is in contradiction with 1., so S cannot be false.

6. Therefore S is true.

7. So the statement "If S is true then God exists" is true.

8. By modus ponens, since S is indeed true, then the second half of that statement is true.

9. God exists.

Note of course that you can make the same argument to prove that God doesn't exist, or anything else.
What, if anything, is wrong with this proof?

*Note: This is the part that I expect most people will comment on. It is one of the standard logical rules that if something, A, is true, you can say "If (~A) then..." and that will always be true. For instance, I could say "If George Washington is alive then the moon is made of cheese" and that would be considered true in natural logic.

 Submitted by Sam Rating: 3.6250 (8 votes) Solution: (Hide) There isn't really a solution to this. It's one of those paradoxes that show holes in our current system of logic (and any possible system of logic). Either step 2 in the argument should not be allowed, which is difficult since a great number of mathematical proofs rely on it, or there is something very troubling with using self-reference in an argument. This paradox, by the way, is a variation on Curry's Paradox, which is similar, and from here you can get to both Lob's theorem and Tarski's theorem, both of which can be used in Godel's proofs.

 Subject Author Date False implies anything Math Man 2011-01-04 18:01:32 re: another solution Sam 2005-03-09 10:30:43 another solution Logan 2005-02-18 10:40:13 Equivocation of S and (S --> G)? Matthew Pianalto 2004-03-09 20:29:07 Comment on solution cogitater 2004-02-02 03:27:52 This statement is false. Jeff 2003-12-23 19:46:02 re(2): Partial disproof Tristan 2003-12-18 22:51:38 Solution DJ 2003-12-18 22:43:01 re: donnmike 2003-12-17 22:07:15 Kripke solved it a long tome ago, Tristan. Penny 2003-12-17 21:40:20 re: Partial disproof SilverKnight 2003-12-17 20:10:18 Partial disproof Tristan 2003-12-17 19:27:29 No Subject stephen ocone 2003-12-17 18:03:06 re: SilverKnight 2003-12-17 16:49:26 No Subject Benjamin J. Ladd 2003-12-17 16:38:44 re(2): God's existence: SilverKnight 2003-12-17 13:35:07 re: God's existence: FatBoy 2003-12-17 08:35:27 re: God's existence: donnmike 2003-12-16 21:03:57 God's existence: Benjamin J. Ladd 2003-12-16 18:40:33 re(3): statement 2 donnmike 2003-12-16 02:05:07 No Subject donnmike 2003-12-16 02:04:22 re(2): statement 2 donnmike 2003-12-15 23:02:37 re: statement 2 Sam 2003-12-15 20:03:01 statement 2 donnmike 2003-12-15 12:24:14 re: The error; re: assumption Sam 2003-12-15 04:43:13 assumption manuel 2003-12-15 02:51:36 my thoughts donnmike 2003-12-15 02:11:29 The error Federico Kereki 2003-12-14 19:35:24 HEY, THEY JUST CAUGHT "GAMER" IN IRAQ !! Penny 2003-12-14 15:16:07 re: Self-referential logic saved my life. Gamer 2003-12-14 14:31:21 Self-referential logic saved my life. Eric 2003-12-14 02:46:32 Has self-referential logic ever achieved anything? Penny 2003-12-14 01:14:03 re(2): Poor Sam...Trying to be a philosopher while ignoring the Ancient Greeks !!!! Penny 2003-12-14 00:37:42 re: Poor Sam...Trying to be a philosopher while ignoring the Ancient Greeks !!!! Sam 2003-12-13 23:01:44 Poor Sam...Trying to be a philosopher while ignoring the Ancient Greeks !!!! Penny 2003-12-13 21:54:10 Penny was right?!?!??! Gamer 2003-12-13 21:45:51 re: Welcome to Logic 101 Sam 2003-12-13 18:09:09 Penny, you missed a chance to impress us... TomM 2003-12-13 18:08:35 proof of anything winnie 2003-12-13 15:58:06 Untying the Gordian Knot Penny 2003-12-13 15:32:40 re(2): Welcome to Logic 101 Penny 2003-12-13 12:29:47 hm.. Victor Zapana 2003-12-13 12:24:00 re: Welcome to Logic 101 Gamer 2003-12-13 10:48:04 Welcome to Logic 101 Penny 2003-12-13 08:58:51

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